Karanka hopes that Given will prolong his stay at the Riverside Stadium now that Steele has picked up an ankle injury.
"We will be having discussions with Aston Villa," Clubcall.com quotes Karanka as saying.
"It depends on what Shay wants and on what Aston Villa want to do, but I would like to have him here for the whole of the season. That would be my choice, but it is not just up to me."
Given has said that he hopes to secure a permanent move away from Villa Park in January.